A Discrete Multi-Tone (DMT) communication system carries information from a transmitter to a receiver over a number of tones. The tones are also commonly referred to as sub-carriers or sub-channels. The transmitter uses a modulation method in which the available bandwidth of a communication channel, such as twisted-pair copper media, is divided into these numerous sub channels.
In the receiver, the data for each sub channel is typically extracted from the time-domain data by taking the Fourier transform of a block of samples from the multi-tone signal. There are various sources of interference and noise in a DMT system that may corrupt the information signal on each tone as it travels through the communication channel and is decoded at the receiver. Because of this signal corruption, the transmitted data may be retrieved erroneously by the receiver. In order to ensure a reliable communication between transmitter and receiver, each tone may carry a limited number of data bits. The number of data bits or the amount of information that a tone carries may vary from tone to tone and depends on the relative power of the information and the corrupting signals on that particular tone.
A reliable communication system is typically defined as a system in which the probability of an erroneously detected data bit by the receiver is always less than a target value. The aggregate sources of corruption associated with each tone are commonly modeled as a single additive noise source with symmetric Gaussian distribution that is added to the information signal on that tone. Under these assumptions, the signal-to-noise power ratio (SNR) becomes a significant factor in determining the maximum number of data bits a tone can carry reliably within a target bit rate error.
The direct relationship between the SNR and the bit rate is based on the key assumption of the symmetry of the Gaussian noise source. However, this assumption may not be completely valid in many practical situations. There are certain types of noise disturbers that cause asymmetry in the distribution of the real and imaginary components of the noise. These noise sources can, for instance, be due to the inter-channel interference from the Nyquist tone—a sub-channel that only carry real component of the signal, or they can be due to ISI of background noise on stop-band frequencies. The effect of these sources become more complicated in a multicarrier system because the Frequency-Domain Equalizer rotates the signal and correlates the real and imaginary component of noise. The Frequency-Domain Equalizer also assumes that a symmetric Gaussian noise source is present in the background noise. With such a complex source of impairment, SNR alone cannot determine the reliable bit rate. In the presence of an asymmetric Gaussian noise source, a typical bit-loading based on the assumption of symmetry may lead to an actual higher error rate than the target bit rate error.